The symmetry axis of image with function f (x) = 3sin (2x - π / 3)

The symmetry axis of image with function f (x) = 3sin (2x - π / 3)

Let 2x - π / 3 = π / 2 + K π (K ∈ z)
The solution is x = 5 / 12 π + K π / 2 (K ∈ z)
So if f (x) = 3sin (2x - π / 3), x = 5 / 12 π + K π / 2 (K ∈ z)

The function y = 3sin (2x + 30) the first axis of symmetry of an image can be
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Y = 3sin (2x + π / 6) = 3sin [2 (x + π / 12)] the image of this function is reduced by one time from the abscissa of the image of y = SiNx, expanded by two times from the ordinate, and shifted π / 12 units to the left. The symmetry axis of y = SiNx is x = k π + π / 2, K ∈ ZY = 3sin2x is x = k π / 2 + π / 4, K ∈ ZY = 3sin [2 (x + π / 12)]

If the function y = 3sin (2x + π 6) is known, then the equation of its axis of symmetry is ()
A. x=0B. x=-π12C. x=π6D. x=π3

From 2x + π 6 = k π + π 2, we can get x = k π 2 + π 6 (K ∈ z), let k = 0, we can get x = π 6, its equation of symmetry axis is x = π 6, so we choose C

What is the nearest axis of symmetry between the function y = 3sin (2x + π / 6) and the Y axis

x=π/6